Question

Simplify square root 72 minus square root 27 plus 2 times the square root of 8 . (5 points) Group of answer choices negative 2 times the square root of 3 plus 5 times the square root of 2 negative 30 times the square root of 6 7 square root of 5 10 times the square root of 2 minus 3 times the square root of 3.

What is the simplified expression for √72 - √27 + 2√8?
A) -2√3 + 5√2
B) -30√6
C) 7√5
D) 10√2 - 3√3

Answer 1

The simplified expression for √72 - √27 + 2√8 is 10√2 - 3√3, after breaking down each square root into its prime factors and simplifying like terms.

Step-by-step explanation:

To simplify the expression √72 - √27 + 2√8, we need to break down each square root into its prime factors and simplify.

The prime factorization of 72 is 23 × 32. The square root of 72 is therefore √(23 × 32) which simplifies to 6√2 because √(22 × 32) = 6 and we are left with one 2 under the radical.

Similarly, the prime factorization of 27 is 33. The square root of 27 is √(33) which simplifies to 3√3.

The prime factorization of 8 is 23. Therefore, 2√8 becomes 2√(23) which simplifies to 4√2.

Combining these simplified terms, we get:

6√2 - 3√3 + 4√2

Combine like terms:

(6√2 + 4√2) - 3√3 = 10√2 - 3√3

Therefore, the simplified expression is 10√2 - 3√3, which corresponds to option D).